The problem of predicting the properties of glass materials has been a longstanding one in the field of glass and glass-ceramic chemistry. Because most glasses and glass-ceramics (referred to collectively herein as “glasses”) contain a relatively large number of components, e.g., three to six or more in many cases, the compositional space is multi-dimensional, making experimental study of the entire space economically impractical. Yet, from melting through to forming, the production of glass articles would clearly benefit from an ability to predict/estimate glass properties based on glass composition or, conversely, to select glass compositions based on desired properties. Likewise, the ability to predict/estimate the behavior of glass articles during use, e.g., during post-forming thermal processing, would be of great value to the art.
Among all the technologically useful properties of a glass-forming system, the viscosity of the melt is undoubtedly among the most important. Every stage of industrial glass production—from the initial melting, mixing, and fining to the final forming operations—requires careful control of viscosity. For example, viscosity controls the rates of melting and of fining in a glass melting tank. Similarly, each glass forming operation, e.g., fiber forming or the final annealing of container glass, requires a certain well-defined viscosity range and consequently a specific temperature range for that operation. See, for example, Varshneya A K (2006) Fundamentals of Inorganic Glasses, 2nd ed. (Society of Glass Technology, Sheffield, UK).
Non-equilibrium viscosity is particularly important with regard to post-forming processing of glass articles. Specifically, non-equilibrium viscosity determines the relaxation rate of a final glass article (final glass product). As just one example, non-equilibrium viscosity controls the compaction behavior of display glasses (e.g., the glass sheets used as substrates in the production of liquid crystal displays) during customer heat treatment cycles. It should thus come as no surprise that the details of the viscosity-temperature-time relationship play a critical role in researching new glass compositions for display and other applications.
Among other reasons, the problem of relating equilibrium viscosity to temperature and composition is challenging because from the initial glass melting to final forming, viscosity varies by over twelve orders of magnitude. See, for example, Varshneya (2006), supra. Equilibrium viscosity is also sensitive to small changes in composition, especially in silicate melts where small levels of impurities can have a profound influence on the flow behavior. It is thus of great importance to have accurate knowledge of the scaling of viscosity with both composition (x) and temperature (T). Unfortunately, measurement of ηeq(T,x) is challenging for high temperature melts, and low temperature measurements (i.e., in the high viscosity range, 1010 to 1015 Pa-s) are time consuming and often prohibitively expensive. See, for example, Varshneya (2006), supra. For non-equilibrium viscosities, the situation is even more complex because in addition to depending on composition (x) and current temperature (T), the non-equilibrium viscosity of a glass article also depends on the glass's thermal history, in particular, its thermal history from that point in time when it was last in thermal equilibrium with its surroundings.
In view of this state of the art, a need exists for more effective methods and apparatus for predicting/estimating the properties of glass materials and, in particular, for predicting/estimating the dependence of viscosity, specifically, non-equilibrium viscosity, on temperature, thermal history, and/or composition. The present disclosure addresses these problems.